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Articles

Articles demonstrate ideas used in production. Every article contains download sample to give a touch to the real world of mathematical ideas used in the modern software.

Corrupted and restored images

Article 1. Median filter

Category. Digital signal and image processing (DSP and DIP) software development.

Median filter is a filter of nonlinear class. This article is a practical guide for understanding and implementation of the filter — it contains theory, C++ source code, programming instructions and sample application. The application demonstrates the capability of the median filter to restore images corrupted by destructive noise. This is not the only kind of corruption the filter can filter out. Download the sample and try this “miracle” of image processing science. Generator of destructive noise and sample image are supplied as well.

Original and rotated images

Article 2. Image rotation

Category. Pixel graphics rendering software development.

That is not so easy to rotate the image in the screen because the screen picture is discrete. So what is the way? One should use special algorithms to calculate antialiased image. This sample demonstrates antialiased image rotation. You can process any 24-bit BMP file.

Demo screenshot

Article 3. Deformation visualization

Category. Scientific graphics rendering software development.

Did you ever interested in question what form had a ball while rebounding from the ground? Do you want to see that? Live mechanics, physics and a bit more. Real-time interactive OpenGL graphics.

Pendulum

Article 4. Pendulum in viscous media

Category. Microcontroller firmware development.

Note. The sample is a part of a production project.

This sample demonstrates solving of the problem of optimal control theory. It is pure MatLab calculation sample.

Original and smoothed images

Article 5. Mean filter, or average filter

Category. Digital signal and image processing (DSP and DIP) software development.

Mean filter, or average filter maybe is the simplest filter of linear class. Nevertheless, it is used widely in signal and image processing, usually as a part of processing pipeline for signal (image) averaging and preparing it for further processing. The article is a practical introduction to this useful tool — it contains theory, C++ source code, programming instructions and sample application for demonstrating filter features.

3D filter window or mask

Article 6. Filter window, or filter mask

Category. Digital signal and image processing (DSP and DIP) software development.

Filter window, or filter mask is basic concept of signal and image processing. Every digital filter utilizes window idea. The article is close look at this important primitive.

Corrupted and restored images

Article 7. Alpha-trimmed mean filter

Category. Digital signal and image processing (DSP and DIP) software development.

Alpha-trimmed mean filter is a filter of nonlinear class, by its nature — hybrid of median and mean filters. This article is a practical tutorial for understanding and implementation of the filter — it contains theory, C++ source code, programming instructions and sample application. The application demonstrates the capability of the alpha-trimmed mean filter to restore images corrupted by impulse noise. Download the sample and try this item. Generator of impulse noise and sample image are provided as well.

Corrupted and restored images

Article 8. Hybrid median filter

Category. Digital image processing (DIP) software development.

Hybrid median filter is a filter of nonlinear class with good corner preserving capabilities. This article is a practical tutorial for understanding and implementation of the filter — it contains theory, C++ source code, programming instructions and sample application. The application demonstrates the capability of the hybrid median filter to restore images corrupted by impulse noise. Download the sample and try this item. Generator of impulse noise and sample image are provided as well.

Original and blurred images

Article 9. Gaussian filter, or Gaussian blur

Category. Digital signal and image processing (DSP and DIP) software development.

Gaussian filter is a filter of linear class, by its nature is weighted mean. Another name for this filter is Gaussian blur. This article is a practical tutorial for understanding and implementation of the filter — it contains theory, C++ source code, programming instructions and sample application. The application demonstrates Gaussian blur application to color images. Download the sample and try this item.

Fast Fourier transform - FFT

Article 10. Fast Fourier transform — FFT

Category. Digital signal processing (DSP) software development.

Fast Fourier transform — FFT — is speed-up technique for calculating DFT — discrete Fourier transform. This article is a practical tutorial for understanding and implementation of FFT — it contains theory, C++ source code and programming instructions. Popular Cooley-Tukey algorithm is considered.

Function handbook

Article 11. Function handbook

Category. Mathematics.

Function handbook contains all trigonometric, hyperbolic and elementary functions: explore their definitions, plots and properties.